added parts of tutorial and proposed solutions 6

[lectures/latex.git] / solid_state_physics / tutorial / 1_06s.tex

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+\pdfoutput=0
+\documentclass[a4paper,11pt]{article}
+\usepackage[activate]{pdfcprot}
+\usepackage{verbatim}
+\usepackage{a4}
+\usepackage{a4wide}
+\usepackage[german]{babel}
+\usepackage[latin1]{inputenc}
+\usepackage[T1]{fontenc}
+\usepackage{amsmath}
+\usepackage{ae}
+\usepackage{aecompl}
+\usepackage[dvips]{graphicx}
+\graphicspath{{./img/}}
+\usepackage{color}
+\usepackage{pstricks}
+\usepackage{pst-node}
+\usepackage{rotating}
+
+\setlength{\headheight}{0mm} \setlength{\headsep}{0mm}
+\setlength{\topskip}{-10mm} \setlength{\textwidth}{17cm}
+\setlength{\oddsidemargin}{-10mm}
+\setlength{\evensidemargin}{-10mm} \setlength{\topmargin}{-1cm}
+\setlength{\textheight}{26cm} \setlength{\headsep}{0cm}
+
+\renewcommand{\labelenumi}{(\alph{enumi})}
+
+\begin{document}
+
+% header
+\begin{center}
+ {\LARGE {\bf Materials Physics I}\\}
+ \vspace{8pt}
+ Prof. B. Stritzker\\
+ WS 2007/08\\
+ \vspace{8pt}
+ {\Large\bf Tutorial 6 - proposed solutions}
+\end{center}
+
+\section{Indirect band gap of silicon}
+
+\begin{enumerate}
+ \item \begin{itemize}
+        \item Photon wavelength:\\
+             $E_g=\hbar\omega=\hbar\frac{2\pi}{T}=\hbar 2\pi v
+                 \stackrel{c=v\lambda}{=}\hbar 2\pi\frac{c}{\lambda}$
+             $\Rightarrow \lambda=\frac{\hbar 2\pi c}{E_g}
+                                 =\frac{hc}{E_g}=\ldots=1.11 \, \mu m$
+       \item Photon momentum:\\
+             $p=\hbar k=\hbar\frac{2\pi}{\lambda}=\frac{h}{\lambda}
+               =\ldots=5.97 \cdot 10^{-28} \, kg\frac{m}{s}$
+       \end{itemize}
+ \item Phonon momentum necessary for transition:\\
+       $p=\hbar \cdot \Delta k=\hbar \cdot 0.85 \, \frac{2\pi}{a}
+         =\frac{0.85 \, h}{a}=\ldots=1.04 \cdot 10^{-24} \, kg\frac{m}{s}$\\
+       $\rightarrow$ Phonon momentum 3 orders of magnitude below
+                     the momentum necessary for transition!
+ \item 
+\end{enumerate}
+
+\section{\ldots}
+
+\ldots
+
+\begin{enumerate}
+ \item \ldots
+ \item \ldots
+\end{enumerate}
+
+\end{document}